Explanation Formula used: If l, m, and n are two solution for the quadratic equation , then the quadratic is ( x − l ) ( x − m ) = 0 . Calculation: The solution set for the polynomial equation is [ − 4 , 3 ] ∪ [ 7 , ∞ ) . The intervals formed by the points − 4 , 3 , and 7 are ( − ∞ , − 4 ) , ( − 4 , 3 ) , ( 3 , 7 ) and ( 7 , ∞ ) . By using the formula, the polynomial equation is ( x + 4 ) ( x − 3 ) ( x − 7 ) = 0 , where l = − 4 , m = 3 and n = 7 . Simplify the above polynomial inequality as follows. ( x + 4 ) ( x − 3 ) ( x − 7 ) = 0 ( x 2 − 3 x + 4 x − 12 ) ( x − 7 ) = 0 ( x 2 + x − 12 ) ( x − 7 ) = 0 x 3 − 6 x 2 − 19 x + 84 = 0 Let the polynomial function is denoted by f ( x ) = x 3 − 6 x 2 − 19 x + 84 . Find the sign of the polynomial function by testing a point in each interval. Obtain the sign of the polynomial function f ( x ) = x 3 − 6 x 2 − 19 x + 84 at the point x = − 5 on an interval ( − ∞ , − 4 ) . f ( − 5 ) = ( − 5 ) 3 − 6 ( − 5 ) 2 − 19 ( − 5 ) + 84 = − 125 − 150 + 95 + 84 = − 96 < 0 Obtain the sign of the polynomial function f ( x ) = x 3 − 6 x 2 − 19 x + 84 at the point x = 0 on an interval ( − 4 , 3 )

College Algebra: Graphs and Models (6th Edition)

6th Edition

ISBN: 9780134179032

Author: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 4.6, Problem 94E

To determine

To write: A polynomial inequality for the solution set [−4,3]∪[7,∞).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.6, Problem 93E

Chapter 4.6, Problem 95E

Students have asked these similar questions

How long is a guy wire reaching from the top of a 15-foot pole to a point on the ground 9-feet from the pole? Question content area bottom Part 1 The guy wire is exactly feet long. (Type an exact answer, using radicals as needed.) Part 2 The guy wire is approximatelyfeet long. (Round to the nearest thousandth.)

Question 6 Not yet answered Marked out of 5.00 Flag question = If (4,6,-11) and (-12,-16,4), = Compute the cross product vx w k

Consider the following vector field v^-> (x,y): v^->(x,y)=2yi−xj What is the magnitude of the vector v⃗ located in point (13,9)? [Provide your answer as an integer number (no fraction). For a decimal number, round your answer to 2 decimal places]

Chapter 4 Solutions

College Algebra: Graphs and Models (6th Edition)

Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 2E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 10E

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

A polynomial inequality for the solution set [ − 4 , 3 ] ∪ [ 7 , ∞ ) .

Solution Summary: The author calculates a polynomial inequality for the solution set left[-4,3right]cup

Videos

To write: A polynomial inequality for the solution set [−4,3]∪[7,∞).

Want to see the full answer?

Chapter 4 Solutions